\documentclass{article}
\usepackage{amsmath}

\newcount{\numerator}
\newcount{\denominator}
\newcount{\gcd}

% compute \gcd and returns reduced \numerator and \denominator
\newcommand{\reduce}[2]% #1=numerator, #2=denominator
{\numerator=#1\relax
	\denominator=#2\relax
	\loop
	\ifnum\numerator<\denominator
		\advance\denominator by -\numerator
		\gcd=\denominator
	\else
		\advance\numerator by -\denominator
		\gcd=\numerator% swap
	\fi
	\ifnum\gcd>1 \repeat
	\ifnum\gcd=0 \gcd=\denominator\fi
	\numerator=#1\relax
	\divide\numerator by \gcd
	\denominator=#2\relax
	\divide\denominator by \gcd
}

\begin{document}

For example, I would like the fraction
\begin{equation*}
	\frac{278922}{74088}
\end{equation*}
to be reduced to\reduce{278922}{74088}
\begin{equation*}
	\frac{\the\numerator}{\the\denominator} =
	\frac{6641}{1764}
\end{equation*}

\end{document}
